Daily Papers

A regular semisimple Hessenberg variety Hess(S,h) is a smooth subvariety of the flag variety determined by a square matrix S with distinct eigenvalues and a Hessenberg function h. The cohomology ring H^*(Hess(S,h)) is independent of the choice of S and is not explicitly described except for a few cases. In this paper, we characterize the Hessenberg function h such that H^*(Hess(S,h)) is generated in degree two as a ring. It turns out that such h is what is called a (double) lollipop.

We reobtain and often refine prior criteria due to Kaplansky, McGovern, Roitman, Shchedryk, Wiegand, and Zabavsky--Bilavska and obtain new criteria for a Hermite ring to be an EDR. We mention three criteria: (1) a Hermite ring R is an EDR iff for all pairs (a,c)in R^2, the product homomorphism U(R/Rac)times Ubigl(R/Rc(1-a)bigr)to U(R/Rc) between groups of units is surjective; (2) a reduced Hermite ring R is an EDR iff it is a pre-Schreier ring and for each ain R, every zero determinant unimodular 2times 2 matrix with entries in R/Ra lifts to a zero determinant matrix with entries in R; (3) a Bézout domain R is an EDD iff for all triples (a,b,c)in R^3 there exists a unimodular pair (e,f)in R^2 such that (a,e) and (be+af,1-a-bc) are unimodular pairs. We use these criteria to show that each Bézout ring R that is an (SU)_2 ring (as introduced by Lorenzini) such that for each nonzero ain R there exists no nontrivial self-dual projective R/Ra-module of rank 1 generated by 2 elements (e.g., all its elements are squares), is an EDR.

This work proposes a new challenge set for multimodal classification, focusing on detecting hate speech in multimodal memes. It is constructed such that unimodal models struggle and only multimodal models can succeed: difficult examples ("benign confounders") are added to the dataset to make it hard to rely on unimodal signals. The task requires subtle reasoning, yet is straightforward to evaluate as a binary classification problem. We provide baseline performance numbers for unimodal models, as well as for multimodal models with various degrees of sophistication. We find that state-of-the-art methods perform poorly compared to humans (64.73% vs. 84.7% accuracy), illustrating the difficulty of the task and highlighting the challenge that this important problem poses to the community.

We introduce Dynabench, an open-source platform for dynamic dataset creation and model benchmarking. Dynabench runs in a web browser and supports human-and-model-in-the-loop dataset creation: annotators seek to create examples that a target model will misclassify, but that another person will not. In this paper, we argue that Dynabench addresses a critical need in our community: contemporary models quickly achieve outstanding performance on benchmark tasks but nonetheless fail on simple challenge examples and falter in real-world scenarios. With Dynabench, dataset creation, model development, and model assessment can directly inform each other, leading to more robust and informative benchmarks. We report on four initial NLP tasks, illustrating these concepts and highlighting the promise of the platform, and address potential objections to dynamic benchmarking as a new standard for the field.